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Year 10 Interactive Maths - Second Edition


Multiplication of Surds

We will consider the multiplication of entire surds and the multiplication of mixed surds.


Multiplication of Entire Surds

In general:

The multiplication of like surds gives a rational number. That is:


Example 11

Solution:

Short way:

Short way:


In general:

The multiplication of unlike surds gives an irrational number.


Example 12

Solution:


Note:

Always give your answer in the simplest possible form.


Multiplication of Mixed Surds

We can get the same result by multiplying the radicands and multiplying the coefficients, as follows:


In general:


Example 13

Solution:

Alternatively:


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